導讀： 資源介紹 語言: 英文 地區: 美國 圖書fenlei: 科技 中文名: 計算接觸力學 發行時間: 2006年01月01日 原名: Computational Contact Mechanics 資源格式: PDF 版本: 掃描版 簡介: Contact mechanics has its appli 資源介紹 語言: 英文 地區: 美國 圖書fenlei: 科技 中文名: 計算接觸力學 發行時間: 2006年01月01日 原名: Computational Contact Mechanics 資源格式: PDF 版本: 掃描版 簡介: Contact mechanics has its application in many engineering problems. No one
can walk without frictional contact, and no car would move for the same reason.
Hence contact mechanics has, from an engineering point of view, a long
history, beginning in ancient Egypt with the movement of large stone blocks,
over first experimental contributions from leading scientists like Leonardo
da Vinci and Coulomb, to today’s computational methods. In the past contact
conditions were often modelled in engineering analysis by more simple
boundary conditions since analytical solutions were not present for real world
applications. In such cases, one investigated contact as a local problem using
the stress and strain fields stemming from the analysis which was performed
for the entire structure. With the rapidly increasing power of modern computers,
more and more numerical simulations in engineering can include contact
constraints directly, which make the problems nonlinear.
This book is an account of the modern theory of nonlinear continuum
mechanics and its application to contact problems, as well as of modern simulation
techniques for contact problems using the finite element method. The
latter includes a variety of discretization techniques for small and large deformation
contact. Algorithms play another prominent role when robust and efficient
techniques have to be designed for contact simulations. Finally, adaptive
methods based on error controlled finite element analysis and mesh adaption
techniques are of great interest for the reliable numerical solution of contact
problems. Nevertheless, all numerical models need a strong backup provided
by modern continuum mechanics and its constitutive theory, which is applied
in this book to the development of interface laws for normal and frictional
contact. 目錄: 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Introduction to Contact Mechanics . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Contact in a Mass Spring System. . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 General formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Lagrange multiplier method . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.3 Penalty method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Finite Element Analysis of the Contact of Two Bars . . . . . . . . . 18
2.3 Thermo-mechanical Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Continuum Solid Mechanics and Weak Forms. . . . . . . . . . . . . . 31
3.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1.1 Motion and deformation gradient . . . . . . . . . . . . . . . . . . . . 31
3.1.2 Strain measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.3 Transformation of vectors and tensors . . . . . . . . . . . . . . . . 36
3.1.4 Time derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 Balance Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.1 Balance of mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.2 Local balance of momentum and moments of momentum 38
3.2.3 First law of thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.4 Transformation to the initial configuration, different
stress tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Weak Form of Balance of Momentum, Variational Principles . . 41
3.3.1 Weak form of balance of momentum in the initial
configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.2 Spatial form of the weak formulation . . . . . . . . . . . . . . . . . 42
3.3.3 Minimum of total potential energy . . . . . . . . . . . . . . . . . . . 43
3.4 Constitutive Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.1 Hyperelastic response function . . . . . . . . . . . . . . . . . . . . . . 44
3.5 Linearizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.5.1 Linearization of kinematical quantities . . . . . . . . . . . . . . . 51
3.5.2 Linearization of constitutive equations . . . . . . . . . . . . . . . 52
3.5.3 Linearization of the weak form . . . . . . . . . . . . . . . . . . . . . . 53
3.5.4 Linearization of a deformation dependent load . . . . . . . . 55
4 Contact Kinematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.1 Normal Contact of Three-dimensional Bodies . . . . . . . . . . . . . . . 58
4.2 Tangential Contact of Three-dimensional Bodies . . . . . . . . . . . . . 62
4.2.1 Stick condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.2 Slip condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3 Variation of the Normal and Tangential Gap . . . . . . . . . . . . . . . . 66
4.3.1 Variation of normal gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3.2 Variation of tangential gap . . . . . . . . . . . . . . . . . . . . . . . . . 67
5 Constitutive Equations for Contact Interfaces . . . . . . . . . . . . . 69
5.1 Normal Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.1.1 Constraint formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.1.2 Constitutive equations for normal contact . . . . . . . . . . . . 72
5.2 Tangential Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2.1 Stick as a constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.2 Coulomb law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.3 Regularization of the Coulomb law . . . . . . . . . . . . . . . . . . 79
5.2.4 Elasto-plastic analogy for friction . . . . . . . . . . . . . . . . . . . . 80
5.2.5 Friction laws for metal forming . . . . . . . . . . . . . . . . . . . . . . 86
5.2.6 Friction laws for rubber and polymers . . . . . . . . . . . . . . . . 88
5.2.7 Friction laws for concrete structures on soil . . . . . . . . . . . 90
5.2.8 Friction laws from computational homogenization
procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3 Lubrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.4 Adhesion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.5 Decohesion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.6 Wear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.7 Fractal Contact Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6 Contact Boundary Value Problem and Weak Form . . . . . . . . 109
6.1 Frictionless Contact in Linear Elasticity . . . . . . . . . . . . . . . . . . . . 109
6.2 Frictionless Contact in Finite Deformations Problems . . . . . . . . 113
6.3 Treatment of Contact Constraints . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.3.1 Lagrange multiplier method . . . . . . . . . . . . . . . . . . . . . . . . 117
6.3.2 Penalty method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.3.3 Direct constraint elimination . . . . . . . . . . . . . . . . . . . . . . . . 120
6.3.4 Constitutive equation in the interface . . . . . . . . . . . . . . . . 121
6.3.5 Nitsche method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122